We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain $\Omega\subset\mathbb{R}^3$. It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient. The solution is uniformly bounded in a conormal Sobolev space and $W^{1,\infty}(\Omega)$ which allows us to take the zero kinematic viscosity-magnetic diffusion limit. Moreover, we also get the rates of convergence in $L^\infty(0,T; L^2)$, $L^\infty(0,T; W^{1,p})\,(2\leq p<\infty)$, and $L^\infty((0,T)\times \Omega)$ for some $T>0$.
Fucai LI
,
Zhipeng ZHANG
. ZERO KINEMATIC VISCOSITY-MAGNETIC DIFFUSION LIMIT OF THE INCOMPRESSIBLE VISCOUS MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS[J]. Acta mathematica scientia, Series B, 2021
, 41(5)
: 1503
-1536
.
DOI: 10.1007/s10473-021-0507-4
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